% Package inclusion and formatting (fold)
%\usepackage{xunicode}

\usepackage[small]{caption}

\usepackage{fullpage}
\usepackage{boxedminipage}

\usepackage{color}
\usepackage{booktabs}
\usepackage{subfig}
\usepackage{float}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{latexsym}
\usepackage{algorithm2e}
\usepackage{textcomp}

\usepackage{array}
\usepackage{tikz}
%\usetikzlibrary{arrows,backgrounds,fit,positioning}
\usetikzlibrary{positioning,fit}

\usepackage[bookmarks=true,colorlinks=true,linkcolor=black,plainpages=false,pdfpagelabels]{hyperref}

% (end)
% TikZ Styles (fold)
\tikzset{normalnode/.style={ 
	circle,draw=blue!50,
	minimum size=5mm,
	fill=blue!20,
	thick
}}
\tikzset{smallnode/.style={ 
	circle,draw=blue!50,
	minimum size=3mm,
	fill=blue!20,
	thick
}}
\tikzset{focusnode/.style={ 
	circle,draw=red!50,
	minimum size=5mm,
	fill=red!20,
	very thick
}}
\tikzset{manynodes/.style={ 
	circle,draw=yellow!60,
	minimum size=10mm,
	fill=yellow!20,
	very thick
}}
% (end)
% Other styles (fold)
\newfloat{example}{htbp}{loe}[section]
\floatname{example}{Example}

\theoremstyle{plain}
\newtheorem{thm}{Theorem} 
\newtheorem{cornum}{Corollary}
\newtheorem*{cor}{Corollary}
\newtheorem{fcon}{False Conjecture}
\newtheorem{lemnum}{Lemma}
\newtheorem*{lem}{Lemma}

\theoremstyle{definition}
\newtheorem{defn}{Definition}
\newtheorem{con}{Conjecture}
\newtheorem{exmp}{Example}

\theoremstyle{remark}
\newtheorem*{rem}{Remark}
\newtheorem*{note}{Note}
\newtheorem{case}{Case}

\theoremstyle{plain}
% (end)
% Custom commands (fold)
\newcommand{\HRule}{\rule{\textwidth}{0.5mm}}
\newcommand{\todo}[1]{\textcolor{red}{\textsf{\bfseries #1}}}
\newcommand{\allclusters}{\ensuremath{\mathcal{C}}}

\newcommand{\argmax}{\operatornamewithlimits{argmax}}

\newcommand{\enclosedin}{\ensuremath{\,\,\bar{\in}\,\,}}
\newcommand{\encloses}{\ensuremath{\,\,\bar{\ni}\,\,}}

\newcommand{\groups}[1]{\ensuremath{G}}
\newcommand{\group}[2]{\ensuremath{G_{#2}}}
\newcommand{\rootgroup}[1]{\group{#1}{0}}
\newcommand{\childgroups}[2]{\ensuremath{C_{#2}}}
\newcommand{\vertices}[2]{\ensuremath{V_{#2}}}
\newcommand{\edgecost}[2]{\ensuremath{\alpha{}_{#2}}}
\newcommand{\edges}[1]{\ensuremath{E}}

\newcommand{\openbullet}{\ensuremath{\mbox{\textopenbullet}}}

\setlength{\parskip}{\baselineskip}
\setlength{\parindent}{0em}

\newcommand{\hh}{\sharp}
\newcommand{\claim}{\textbf{Theorem.}}
\newcommand{\bproof}{\begin{proof}}
\newcommand{\eproof}{\end{proof} \vspace{20pt}}
\newcommand{\bigH}{\mathcal{H}}
\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor}
\newcommand{\ceil}[1]{\left\lceil #1 \right\rceil}
\newcommand{\eadd}[2]{\Delta_{ #1 \stackrel{+}{\rightarrow} #2 }}
\newcommand{\erem}[2]{\Delta_{ #1 \stackrel{-}{\rightarrow} #2 }}
\newcommand{\deltav}[4]{\Delta \stackrel{ #1 #2 }{v}(#3 , #4 )}
% (end)